\(\renewcommand{\hat}[1]{\widehat{#1}}\)

Shared Qs (u11)


  1. Question

    The 2D distance formula is an equivalent equation to the Pythagorean equation. When finding distance between two points on an \(xy\)-plane, it can be helpful to imagine a right triangle with its legs horizontal and vertical, and its hypotenuse connecting the points. The length of the hypotenuse is the square root of the sum of the squares of the legs’ lengths. Each leg’s length is found by taking an absolute difference corresponding coordinates; for example \(|x_2-x_1|\) is the length of the horizontal leg, and \(|y_2-y_1|\) is the length of the vertical leg.

    A square field is 200 feet by 200 feet. The field is marked with a grid pattern, so the Southwest corner is at point \((0,0)\) and the Northeast corner is at point \((200,200)\). Near the middle, at position \((94, 97)\) is a beacon, marked as a large bright-red dot. On the field are 5 players; their positions are listed in the table below. Find how far each player is from the beacon.

    plot of chunk unnamed-chunk-28

    I would recommend setting this up in Desmos using \(d=\sqrt{(x_2-94)^2+(y_2-97)^2}\) and using sliders for \(x_2\) and \(y_2\).

    Player Position Distance to beacon (ft)
    1 (90,94)
    2 (38,55)
    3 (99,109)
    4 (64,57)
    5 (114,76)


    Solution


  2. Question

    The 2D distance formula is an equivalent equation to the Pythagorean equation. When finding distance between two points on an \(xy\)-plane, it can be helpful to imagine a right triangle with its legs horizontal and vertical, and its hypotenuse connecting the points. The length of the hypotenuse is the square root of the sum of the squares of the legs’ lengths. Each leg’s length is found by taking an absolute difference corresponding coordinates; for example \(|x_2-x_1|\) is the length of the horizontal leg, and \(|y_2-y_1|\) is the length of the vertical leg.

    A square field is 200 feet by 200 feet. The field is marked with a grid pattern, so the Southwest corner is at point \((0,0)\) and the Northeast corner is at point \((200,200)\). Near the middle, at position \((102, 105)\) is a beacon, marked as a large bright-red dot. On the field are 5 players; their positions are listed in the table below. Find how far each player is from the beacon.

    plot of chunk unnamed-chunk-1

    I would recommend setting this up in Desmos using \(d=\sqrt{(x_2-102)^2+(y_2-105)^2}\) and using sliders for \(x_2\) and \(y_2\).

    Player Position Distance to beacon (ft)
    1 (126,112)
    2 (142,114)
    3 (22,45)
    4 (120,81)
    5 (105,109)


    Solution


  3. Question

    The 2D distance formula is an equivalent equation to the Pythagorean equation. When finding distance between two points on an \(xy\)-plane, it can be helpful to imagine a right triangle with its legs horizontal and vertical, and its hypotenuse connecting the points. The length of the hypotenuse is the square root of the sum of the squares of the legs’ lengths. Each leg’s length is found by taking an absolute difference corresponding coordinates; for example \(|x_2-x_1|\) is the length of the horizontal leg, and \(|y_2-y_1|\) is the length of the vertical leg.

    A square field is 200 feet by 200 feet. The field is marked with a grid pattern, so the Southwest corner is at point \((0,0)\) and the Northeast corner is at point \((200,200)\). Near the middle, at position \((103, 98)\) is a beacon, marked as a large bright-red dot. On the field are 5 players; their positions are listed in the table below. Find how far each player is from the beacon.

    plot of chunk unnamed-chunk-1

    I would recommend setting this up in Desmos using \(d=\sqrt{(x_2-103)^2+(y_2-98)^2}\) and using sliders for \(x_2\) and \(y_2\).

    Player Position Distance to beacon (ft)
    1 (43,123)
    2 (43,178)
    3 (113,122)
    4 (52,30)
    5 (58,74)


    Solution


  4. Question

    The 2D distance formula is an equivalent equation to the Pythagorean equation. When finding distance between two points on an \(xy\)-plane, it can be helpful to imagine a right triangle with its legs horizontal and vertical, and its hypotenuse connecting the points. The length of the hypotenuse is the square root of the sum of the squares of the legs’ lengths. Each leg’s length is found by taking an absolute difference corresponding coordinates; for example \(|x_2-x_1|\) is the length of the horizontal leg, and \(|y_2-y_1|\) is the length of the vertical leg.

    A square field is 200 feet by 200 feet. The field is marked with a grid pattern, so the Southwest corner is at point \((0,0)\) and the Northeast corner is at point \((200,200)\). Near the middle, at position \((91, 101)\) is a beacon, marked as a large bright-red dot. On the field are 5 players; their positions are listed in the table below. Find how far each player is from the beacon.

    plot of chunk unnamed-chunk-1

    I would recommend setting this up in Desmos using \(d=\sqrt{(x_2-91)^2+(y_2-101)^2}\) and using sliders for \(x_2\) and \(y_2\).

    Player Position Distance to beacon (ft)
    1 (61,173)
    2 (131,92)
    3 (154,161)
    4 (103,66)
    5 (109,181)


    Solution


  5. Question

    The 2D distance formula is an equivalent equation to the Pythagorean equation. When finding distance between two points on an \(xy\)-plane, it can be helpful to imagine a right triangle with its legs horizontal and vertical, and its hypotenuse connecting the points. The length of the hypotenuse is the square root of the sum of the squares of the legs’ lengths. Each leg’s length is found by taking an absolute difference corresponding coordinates; for example \(|x_2-x_1|\) is the length of the horizontal leg, and \(|y_2-y_1|\) is the length of the vertical leg.

    A square field is 200 feet by 200 feet. The field is marked with a grid pattern, so the Southwest corner is at point \((0,0)\) and the Northeast corner is at point \((200,200)\). Near the middle, at position \((104, 107)\) is a beacon, marked as a large bright-red dot. On the field are 5 players; their positions are listed in the table below. Find how far each player is from the beacon.

    plot of chunk unnamed-chunk-1

    I would recommend setting this up in Desmos using \(d=\sqrt{(x_2-104)^2+(y_2-107)^2}\) and using sliders for \(x_2\) and \(y_2\).

    Player Position Distance to beacon (ft)
    1 (92,116)
    2 (83,35)
    3 (71,163)
    4 (124,59)
    5 (8,135)


    Solution


  6. Question

    The 2D distance formula is an equivalent equation to the Pythagorean equation. When finding distance between two points on an \(xy\)-plane, it can be helpful to imagine a right triangle with its legs horizontal and vertical, and its hypotenuse connecting the points. The length of the hypotenuse is the square root of the sum of the squares of the legs’ lengths. Each leg’s length is found by taking an absolute difference corresponding coordinates; for example \(|x_2-x_1|\) is the length of the horizontal leg, and \(|y_2-y_1|\) is the length of the vertical leg.

    A square field is 200 feet by 200 feet. The field is marked with a grid pattern, so the Southwest corner is at point \((0,0)\) and the Northeast corner is at point \((200,200)\). Near the middle, at position \((92, 109)\) is a beacon, marked as a large bright-red dot. On the field are 5 players; their positions are listed in the table below. Find how far each player is from the beacon.

    plot of chunk unnamed-chunk-1

    I would recommend setting this up in Desmos using \(d=\sqrt{(x_2-92)^2+(y_2-109)^2}\) and using sliders for \(x_2\) and \(y_2\).

    Player Position Distance to beacon (ft)
    1 (35,33)
    2 (71,37)
    3 (48,142)
    4 (107,101)
    5 (148,151)


    Solution


  7. Question

    The 2D distance formula is an equivalent equation to the Pythagorean equation. When finding distance between two points on an \(xy\)-plane, it can be helpful to imagine a right triangle with its legs horizontal and vertical, and its hypotenuse connecting the points. The length of the hypotenuse is the square root of the sum of the squares of the legs’ lengths. Each leg’s length is found by taking an absolute difference corresponding coordinates; for example \(|x_2-x_1|\) is the length of the horizontal leg, and \(|y_2-y_1|\) is the length of the vertical leg.

    A square field is 200 feet by 200 feet. The field is marked with a grid pattern, so the Southwest corner is at point \((0,0)\) and the Northeast corner is at point \((200,200)\). Near the middle, at position \((107, 95)\) is a beacon, marked as a large bright-red dot. On the field are 5 players; their positions are listed in the table below. Find how far each player is from the beacon.

    plot of chunk unnamed-chunk-1

    I would recommend setting this up in Desmos using \(d=\sqrt{(x_2-107)^2+(y_2-95)^2}\) and using sliders for \(x_2\) and \(y_2\).

    Player Position Distance to beacon (ft)
    1 (83,25)
    2 (75,71)
    3 (95,100)
    4 (131,105)
    5 (11,67)


    Solution


  8. Question

    The 2D distance formula is an equivalent equation to the Pythagorean equation. When finding distance between two points on an \(xy\)-plane, it can be helpful to imagine a right triangle with its legs horizontal and vertical, and its hypotenuse connecting the points. The length of the hypotenuse is the square root of the sum of the squares of the legs’ lengths. Each leg’s length is found by taking an absolute difference corresponding coordinates; for example \(|x_2-x_1|\) is the length of the horizontal leg, and \(|y_2-y_1|\) is the length of the vertical leg.

    A square field is 200 feet by 200 feet. The field is marked with a grid pattern, so the Southwest corner is at point \((0,0)\) and the Northeast corner is at point \((200,200)\). Near the middle, at position \((99, 109)\) is a beacon, marked as a large bright-red dot. On the field are 5 players; their positions are listed in the table below. Find how far each player is from the beacon.

    plot of chunk unnamed-chunk-1

    I would recommend setting this up in Desmos using \(d=\sqrt{(x_2-99)^2+(y_2-109)^2}\) and using sliders for \(x_2\) and \(y_2\).

    Player Position Distance to beacon (ft)
    1 (144,169)
    2 (87,93)
    3 (115,46)
    4 (95,112)
    5 (129,125)


    Solution


  9. Question

    The 2D distance formula is an equivalent equation to the Pythagorean equation. When finding distance between two points on an \(xy\)-plane, it can be helpful to imagine a right triangle with its legs horizontal and vertical, and its hypotenuse connecting the points. The length of the hypotenuse is the square root of the sum of the squares of the legs’ lengths. Each leg’s length is found by taking an absolute difference corresponding coordinates; for example \(|x_2-x_1|\) is the length of the horizontal leg, and \(|y_2-y_1|\) is the length of the vertical leg.

    A square field is 200 feet by 200 feet. The field is marked with a grid pattern, so the Southwest corner is at point \((0,0)\) and the Northeast corner is at point \((200,200)\). Near the middle, at position \((95, 102)\) is a beacon, marked as a large bright-red dot. On the field are 5 players; their positions are listed in the table below. Find how far each player is from the beacon.

    plot of chunk unnamed-chunk-1

    I would recommend setting this up in Desmos using \(d=\sqrt{(x_2-95)^2+(y_2-102)^2}\) and using sliders for \(x_2\) and \(y_2\).

    Player Position Distance to beacon (ft)
    1 (35,57)
    2 (149,30)
    3 (86,62)
    4 (172,138)
    5 (115,123)


    Solution


  10. Question

    The 2D distance formula is an equivalent equation to the Pythagorean equation. When finding distance between two points on an \(xy\)-plane, it can be helpful to imagine a right triangle with its legs horizontal and vertical, and its hypotenuse connecting the points. The length of the hypotenuse is the square root of the sum of the squares of the legs’ lengths. Each leg’s length is found by taking an absolute difference corresponding coordinates; for example \(|x_2-x_1|\) is the length of the horizontal leg, and \(|y_2-y_1|\) is the length of the vertical leg.

    A square field is 200 feet by 200 feet. The field is marked with a grid pattern, so the Southwest corner is at point \((0,0)\) and the Northeast corner is at point \((200,200)\). Near the middle, at position \((105, 95)\) is a beacon, marked as a large bright-red dot. On the field are 5 players; their positions are listed in the table below. Find how far each player is from the beacon.

    plot of chunk unnamed-chunk-1

    I would recommend setting this up in Desmos using \(d=\sqrt{(x_2-105)^2+(y_2-95)^2}\) and using sliders for \(x_2\) and \(y_2\).

    Player Position Distance to beacon (ft)
    1 (90,87)
    2 (54,27)
    3 (181,152)
    4 (121,125)
    5 (98,71)


    Solution


  11. Question

    Using Desmos, determine which of the given points are within a distance of 11 units from point (3, 5).

    1. Graph the inequality \((x-3)^2+(y-5)^2~\le~11^2\) as the first item in Desmos.
    2. Enter each point as a Cartesian coordinate pair. Actually, you should be able to copy/paste all the points as a single item (using commas to separate the points):
      • (12,11), (11,14), (7,16), (-1,14), (-5,12), (-8,2), (-7,1), (-2,-5), (8,-5), (15,2)
    3. Click “Label” to label the points.
    4. Determine which points are in the shaded area. If a point is exactly on the boundary, count that point as within the distance. You might need to zoom in on points to be sure.

    1. (12,11)
    2. (11,14)
    3. (7,16)
    4. (-1,14)
    5. (-5,12)
    6. (-8,2)
    7. (-7,1)
    8. (-2,-5)
    9. (8,-5)
    10. (15,2)

    Solution


  12. Question

    Using Desmos, determine which of the given points are within a distance of 11 units from point (6, 4).

    1. Graph the inequality \((x-6)^2+(y-4)^2~\le~11^2\) as the first item in Desmos.
    2. Enter each point as a Cartesian coordinate pair. Actually, you should be able to copy/paste all the points as a single item (using commas to separate the points):
      • (17,9), (9,13), (4,15), (-1,11), (-3,10), (-3,0), (-3,-5), (5,-7), (12,-6), (18,2)
    3. Click “Label” to label the points.
    4. Determine which points are in the shaded area. If a point is exactly on the boundary, count that point as within the distance. You might need to zoom in on points to be sure.

    1. (17,9)
    2. (9,13)
    3. (4,15)
    4. (-1,11)
    5. (-3,10)
    6. (-3,0)
    7. (-3,-5)
    8. (5,-7)
    9. (12,-6)
    10. (18,2)

    Solution


  13. Question

    Using Desmos, determine which of the given points are within a distance of 8 units from point (-6, 1).

    1. Graph the inequality \((x+6)^2+(y-1)^2~\le~8^2\) as the first item in Desmos.
    2. Enter each point as a Cartesian coordinate pair. Actually, you should be able to copy/paste all the points as a single item (using commas to separate the points):
      • (3,3), (-2,7), (-6,8), (-9,7), (-12,4), (-14,-2), (-9,-6), (-3,-8), (2,-2), (2,-1)
    3. Click “Label” to label the points.
    4. Determine which points are in the shaded area. If a point is exactly on the boundary, count that point as within the distance. You might need to zoom in on points to be sure.

    1. (3,3)
    2. (-2,7)
    3. (-6,8)
    4. (-9,7)
    5. (-12,4)
    6. (-14,-2)
    7. (-9,-6)
    8. (-3,-8)
    9. (2,-2)
    10. (2,-1)

    Solution


  14. Question

    Using Desmos, determine which of the given points are within a distance of 15 units from point (5, -1).

    1. Graph the inequality \((x-5)^2+(y+1)^2~\le~15^2\) as the first item in Desmos.
    2. Enter each point as a Cartesian coordinate pair. Actually, you should be able to copy/paste all the points as a single item (using commas to separate the points):
      • (18,9), (16,9), (4,14), (-6,10), (-10,-2), (-4,-13), (3,-17), (9,-14), (20,-7), (20,-3)
    3. Click “Label” to label the points.
    4. Determine which points are in the shaded area. If a point is exactly on the boundary, count that point as within the distance. You might need to zoom in on points to be sure.

    1. (18,9)
    2. (16,9)
    3. (4,14)
    4. (-6,10)
    5. (-10,-2)
    6. (-4,-13)
    7. (3,-17)
    8. (9,-14)
    9. (20,-7)
    10. (20,-3)

    Solution


  15. Question

    Using Desmos, determine which of the given points are within a distance of 8 units from point (-2, -3).

    1. Graph the inequality \((x+2)^2+(y+3)^2~\le~8^2\) as the first item in Desmos.
    2. Enter each point as a Cartesian coordinate pair. Actually, you should be able to copy/paste all the points as a single item (using commas to separate the points):
      • (6,-3), (4,5), (1,6), (-6,4), (-10,2), (-11,-4), (-9,-5), (-6,-9), (2,-10), (5,-8)
    3. Click “Label” to label the points.
    4. Determine which points are in the shaded area. If a point is exactly on the boundary, count that point as within the distance. You might need to zoom in on points to be sure.

    1. (6,-3)
    2. (4,5)
    3. (1,6)
    4. (-6,4)
    5. (-10,2)
    6. (-11,-4)
    7. (-9,-5)
    8. (-6,-9)
    9. (2,-10)
    10. (5,-8)

    Solution


  16. Question

    Using Desmos, determine which of the given points are within a distance of 15 units from point (6, -8).

    1. Graph the inequality \((x-6)^2+(y+8)^2~\le~15^2\) as the first item in Desmos.
    2. Enter each point as a Cartesian coordinate pair. Actually, you should be able to copy/paste all the points as a single item (using commas to separate the points):
      • (18,-1), (15,5), (3,5), (-8,1), (-9,-8), (-9,-9), (-2,-22), (9,-22), (21,-14), (20,-9)
    3. Click “Label” to label the points.
    4. Determine which points are in the shaded area. If a point is exactly on the boundary, count that point as within the distance. You might need to zoom in on points to be sure.

    1. (18,-1)
    2. (15,5)
    3. (3,5)
    4. (-8,1)
    5. (-9,-8)
    6. (-9,-9)
    7. (-2,-22)
    8. (9,-22)
    9. (21,-14)
    10. (20,-9)

    Solution


  17. Question

    Using Desmos, determine which of the given points are within a distance of 10 units from point (3, 2).

    1. Graph the inequality \((x-3)^2+(y-2)^2~\le~10^2\) as the first item in Desmos.
    2. Enter each point as a Cartesian coordinate pair. Actually, you should be able to copy/paste all the points as a single item (using commas to separate the points):
      • (12,6), (2,12), (-2,11), (-6,8), (-6,1), (-2,-6), (0,-7), (5,-8), (4,-7), (11,-3)
    3. Click “Label” to label the points.
    4. Determine which points are in the shaded area. If a point is exactly on the boundary, count that point as within the distance. You might need to zoom in on points to be sure.

    1. (12,6)
    2. (2,12)
    3. (-2,11)
    4. (-6,8)
    5. (-6,1)
    6. (-2,-6)
    7. (0,-7)
    8. (5,-8)
    9. (4,-7)
    10. (11,-3)

    Solution


  18. Question

    Using Desmos, determine which of the given points are within a distance of 15 units from point (7, 4).

    1. Graph the inequality \((x-7)^2+(y-4)^2~\le~15^2\) as the first item in Desmos.
    2. Enter each point as a Cartesian coordinate pair. Actually, you should be able to copy/paste all the points as a single item (using commas to separate the points):
      • (21,7), (17,15), (2,18), (-8,8), (-7,-4), (-1,-8), (1,-8), (4,-9), (13,-11), (20,-4)
    3. Click “Label” to label the points.
    4. Determine which points are in the shaded area. If a point is exactly on the boundary, count that point as within the distance. You might need to zoom in on points to be sure.

    1. (21,7)
    2. (17,15)
    3. (2,18)
    4. (-8,8)
    5. (-7,-4)
    6. (-1,-8)
    7. (1,-8)
    8. (4,-9)
    9. (13,-11)
    10. (20,-4)

    Solution


  19. Question

    Using Desmos, determine which of the given points are within a distance of 15 units from point (8, -4).

    1. Graph the inequality \((x-8)^2+(y+4)^2~\le~15^2\) as the first item in Desmos.
    2. Enter each point as a Cartesian coordinate pair. Actually, you should be able to copy/paste all the points as a single item (using commas to separate the points):
      • (24,-3), (16,9), (2,10), (-4,4), (-7,-1), (-4,-12), (8,-19), (9,-18), (17,-14), (22,-5)
    3. Click “Label” to label the points.
    4. Determine which points are in the shaded area. If a point is exactly on the boundary, count that point as within the distance. You might need to zoom in on points to be sure.

    1. (24,-3)
    2. (16,9)
    3. (2,10)
    4. (-4,4)
    5. (-7,-1)
    6. (-4,-12)
    7. (8,-19)
    8. (9,-18)
    9. (17,-14)
    10. (22,-5)

    Solution


  20. Question

    Using Desmos, determine which of the given points are within a distance of 13 units from point (-2, -7).

    1. Graph the inequality \((x+2)^2+(y+7)^2~\le~13^2\) as the first item in Desmos.
    2. Enter each point as a Cartesian coordinate pair. Actually, you should be able to copy/paste all the points as a single item (using commas to separate the points):
      • (12,-7), (11,-5), (2,6), (-8,4), (-13,-2), (-15,-3), (-15,-8), (-10,-17), (0,-21), (6,-15)
    3. Click “Label” to label the points.
    4. Determine which points are in the shaded area. If a point is exactly on the boundary, count that point as within the distance. You might need to zoom in on points to be sure.

    1. (12,-7)
    2. (11,-5)
    3. (2,6)
    4. (-8,4)
    5. (-13,-2)
    6. (-15,-3)
    7. (-15,-8)
    8. (-10,-17)
    9. (0,-21)
    10. (6,-15)

    Solution


  21. Question

    Consider the points listed below:

    Please determine which points satisfy both criteria below:

    1. Closer than 16 units from point (32, 42), and
    2. Closer than 9 units from point (48, 50).

    1. (43,48)
    2. (45,45)
    3. (47,39)
    4. (36,57)
    5. (49,52)
    6. (44,47)
    7. (50,49)
    8. (39,56)
    9. (37,50)
    10. (46,40)

    Solution


  22. Question

    Consider the points listed below:

    Please determine which points satisfy both criteria below:

    1. Closer than 20 units from point (56, 66), and
    2. Closer than 14 units from point (81, 69).

    1. (68,67)
    2. (71,61)
    3. (73,62)
    4. (63,69)
    5. (69,73)
    6. (80,65)
    7. (67,77)
    8. (75,70)
    9. (70,66)
    10. (74,75)

    Solution


  23. Question

    Consider the points listed below:

    Please determine which points satisfy both criteria below:

    1. Closer than 12 units from point (74, 15), and
    2. Closer than 27 units from point (54, 42).

    1. (76,28)
    2. (69,22)
    3. (71,14)
    4. (70,29)
    5. (68,20)
    6. (65,30)
    7. (63,24)
    8. (66,19)
    9. (59,18)
    10. (67,17)

    Solution


  24. Question

    Consider the points listed below:

    Please determine which points satisfy both criteria below:

    1. Closer than 22 units from point (51, 66), and
    2. Closer than 15 units from point (80, 58).

    1. (71,58)
    2. (61,66)
    3. (69,69)
    4. (73,57)
    5. (75,52)
    6. (70,61)
    7. (68,56)
    8. (76,70)
    9. (63,62)
    10. (78,64)

    Solution


  25. Question

    Consider the points listed below:

    Please determine which points satisfy both criteria below:

    1. Closer than 15 units from point (18, 73), and
    2. Closer than 22 units from point (30, 46).

    1. (29,59)
    2. (21,65)
    3. (13,70)
    4. (15,68)
    5. (27,63)
    6. (17,71)
    7. (16,64)
    8. (31,67)
    9. (24,69)
    10. (28,56)

    Solution


  26. Question

    Consider the points listed below:

    Please determine which points satisfy both criteria below:

    1. Closer than 15 units from point (54, 45), and
    2. Closer than 14 units from point (77, 49).

    1. (65,53)
    2. (67,42)
    3. (68,49)
    4. (62,48)
    5. (75,41)
    6. (59,44)
    7. (58,56)
    8. (74,38)
    9. (72,45)
    10. (73,47)

    Solution


  27. Question

    Consider the points listed below:

    Please determine which points satisfy both criteria below:

    1. Closer than 14 units from point (82, 26), and
    2. Closer than 22 units from point (61, 49).

    1. (76,34)
    2. (77,42)
    3. (75,37)
    4. (65,38)
    5. (72,30)
    6. (80,29)
    7. (78,43)
    8. (74,31)
    9. (69,36)
    10. (73,41)

    Solution


  28. Question

    Consider the points listed below:

    Please determine which points satisfy both criteria below:

    1. Closer than 15 units from point (25, 19), and
    2. Closer than 15 units from point (37, 39).

    1. (32,30)
    2. (25,27)
    3. (40,36)
    4. (23,29)
    5. (38,31)
    6. (39,23)
    7. (33,39)
    8. (36,28)
    9. (34,25)
    10. (27,26)

    Solution


  29. Question

    Consider the points listed below:

    Please determine which points satisfy both criteria below:

    1. Closer than 11 units from point (13, 24), and
    2. Closer than 22 units from point (29, 43).

    1. (11,22)
    2. (12,34)
    3. (22,37)
    4. (25,29)
    5. (19,38)
    6. (10,32)
    7. (27,24)
    8. (18,31)
    9. (24,36)
    10. (15,27)

    Solution


  30. Question

    Consider the points listed below:

    Please determine which points satisfy both criteria below:

    1. Closer than 28 units from point (30, 62), and
    2. Closer than 12 units from point (53, 84).

    1. (45,76)
    2. (48,70)
    3. (49,87)
    4. (46,80)
    5. (44,85)
    6. (40,79)
    7. (55,75)
    8. (41,71)
    9. (42,69)
    10. (56,81)

    Solution


  31. Question

    A circle has a center and a radius. The distance from the center to any point on the edge equals the radius.

    In Desmos, we can graph a circle using an equation that looks like the Pythagorean equation and the 2D distance formula. If the center is at \((h,k)\) and the radius equals \(r\), the following equation graphs the desired circle in an \(xy\)-plane.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    A large square lake is 200 miles across. The positions of 3 lighthouses are known, as well as the distance from each lighthouse to a boat.

    lighthouse position (miles, miles) distance to boat (miles)
    1 \((139,44)\) \(60\)
    2 \((43,137)\) \(75\)
    3 \((47,59)\) \(65\)

    Use trilateration to find the position of the boat:

    (, )



    Solution


  32. Question

    A circle has a center and a radius. The distance from the center to any point on the edge equals the radius.

    In Desmos, we can graph a circle using an equation that looks like the Pythagorean equation and the 2D distance formula. If the center is at \((h,k)\) and the radius equals \(r\), the following equation graphs the desired circle in an \(xy\)-plane.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    A large square lake is 200 miles across. The positions of 3 lighthouses are known, as well as the distance from each lighthouse to a boat.

    lighthouse position (miles, miles) distance to boat (miles)
    1 \((51,125)\) \(50\)
    2 \((80,155)\) \(61\)
    3 \((130,15)\) \(89\)

    Use trilateration to find the position of the boat:

    (, )



    Solution


  33. Question

    A circle has a center and a radius. The distance from the center to any point on the edge equals the radius.

    In Desmos, we can graph a circle using an equation that looks like the Pythagorean equation and the 2D distance formula. If the center is at \((h,k)\) and the radius equals \(r\), the following equation graphs the desired circle in an \(xy\)-plane.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    A large square lake is 200 miles across. The positions of 3 lighthouses are known, as well as the distance from each lighthouse to a boat.

    lighthouse position (miles, miles) distance to boat (miles)
    1 \((60,169)\) \(80\)
    2 \((48,185)\) \(100\)
    3 \((171,89)\) \(65\)

    Use trilateration to find the position of the boat:

    (, )



    Solution


  34. Question

    A circle has a center and a radius. The distance from the center to any point on the edge equals the radius.

    In Desmos, we can graph a circle using an equation that looks like the Pythagorean equation and the 2D distance formula. If the center is at \((h,k)\) and the radius equals \(r\), the following equation graphs the desired circle in an \(xy\)-plane.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    A large square lake is 200 miles across. The positions of 3 lighthouses are known, as well as the distance from each lighthouse to a boat.

    lighthouse position (miles, miles) distance to boat (miles)
    1 \((30,77)\) \(74\)
    2 \((110,77)\) \(26\)
    3 \((125,161)\) \(65\)

    Use trilateration to find the position of the boat:

    (, )



    Solution


  35. Question

    A circle has a center and a radius. The distance from the center to any point on the edge equals the radius.

    In Desmos, we can graph a circle using an equation that looks like the Pythagorean equation and the 2D distance formula. If the center is at \((h,k)\) and the radius equals \(r\), the following equation graphs the desired circle in an \(xy\)-plane.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    A large square lake is 200 miles across. The positions of 3 lighthouses are known, as well as the distance from each lighthouse to a boat.

    lighthouse position (miles, miles) distance to boat (miles)
    1 \((83,95)\) \(20\)
    2 \((159,62)\) \(75\)
    3 \((134,23)\) \(91\)

    Use trilateration to find the position of the boat:

    (, )



    Solution


  36. Question

    A circle has a center and a radius. The distance from the center to any point on the edge equals the radius.

    In Desmos, we can graph a circle using an equation that looks like the Pythagorean equation and the 2D distance formula. If the center is at \((h,k)\) and the radius equals \(r\), the following equation graphs the desired circle in an \(xy\)-plane.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    A large square lake is 200 miles across. The positions of 3 lighthouses are known, as well as the distance from each lighthouse to a boat.

    lighthouse position (miles, miles) distance to boat (miles)
    1 \((145,136)\) \(55\)
    2 \((119,79)\) \(30\)
    3 \((96,91)\) \(13\)

    Use trilateration to find the position of the boat:

    (, )



    Solution


  37. Question

    A circle has a center and a radius. The distance from the center to any point on the edge equals the radius.

    In Desmos, we can graph a circle using an equation that looks like the Pythagorean equation and the 2D distance formula. If the center is at \((h,k)\) and the radius equals \(r\), the following equation graphs the desired circle in an \(xy\)-plane.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    A large square lake is 200 miles across. The positions of 3 lighthouses are known, as well as the distance from each lighthouse to a boat.

    lighthouse position (miles, miles) distance to boat (miles)
    1 \((131,51)\) \(50\)
    2 \((114,175)\) \(85\)
    3 \((96,103)\) \(13\)

    Use trilateration to find the position of the boat:

    (, )



    Solution


  38. Question

    A circle has a center and a radius. The distance from the center to any point on the edge equals the radius.

    In Desmos, we can graph a circle using an equation that looks like the Pythagorean equation and the 2D distance formula. If the center is at \((h,k)\) and the radius equals \(r\), the following equation graphs the desired circle in an \(xy\)-plane.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    A large square lake is 200 miles across. The positions of 3 lighthouses are known, as well as the distance from each lighthouse to a boat.

    lighthouse position (miles, miles) distance to boat (miles)
    1 \((89,129)\) \(39\)
    2 \((44,118)\) \(65\)
    3 \((119,73)\) \(25\)

    Use trilateration to find the position of the boat:

    (, )



    Solution


  39. Question

    A circle has a center and a radius. The distance from the center to any point on the edge equals the radius.

    In Desmos, we can graph a circle using an equation that looks like the Pythagorean equation and the 2D distance formula. If the center is at \((h,k)\) and the radius equals \(r\), the following equation graphs the desired circle in an \(xy\)-plane.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    A large square lake is 200 miles across. The positions of 3 lighthouses are known, as well as the distance from each lighthouse to a boat.

    lighthouse position (miles, miles) distance to boat (miles)
    1 \((178,44)\) \(90\)
    2 \((134,143)\) \(53\)
    3 \((66,89)\) \(41\)

    Use trilateration to find the position of the boat:

    (, )



    Solution


  40. Question

    A circle has a center and a radius. The distance from the center to any point on the edge equals the radius.

    In Desmos, we can graph a circle using an equation that looks like the Pythagorean equation and the 2D distance formula. If the center is at \((h,k)\) and the radius equals \(r\), the following equation graphs the desired circle in an \(xy\)-plane.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    A large square lake is 200 miles across. The positions of 3 lighthouses are known, as well as the distance from each lighthouse to a boat.

    lighthouse position (miles, miles) distance to boat (miles)
    1 \((112,103)\) \(5\)
    2 \((75,62)\) \(55\)
    3 \((144,133)\) \(45\)

    Use trilateration to find the position of the boat:

    (, )



    Solution


  41. Question

    Consider the triangle with vertices at the following coordinates:

    plot of chunk unnamed-chunk-1

    Calculate the perimeter. Please be accurate to within 0.01 units.


    Solution


  42. Question

    Consider the triangle with vertices at the following coordinates:

    plot of chunk unnamed-chunk-1

    Calculate the perimeter. Please be accurate to within 0.01 units.


    Solution


  43. Question

    Consider the triangle with vertices at the following coordinates:

    plot of chunk unnamed-chunk-1

    Calculate the perimeter. Please be accurate to within 0.01 units.


    Solution


  44. Question

    Consider the triangle with vertices at the following coordinates:

    plot of chunk unnamed-chunk-1

    Calculate the perimeter. Please be accurate to within 0.01 units.


    Solution


  45. Question

    Consider the triangle with vertices at the following coordinates:

    plot of chunk unnamed-chunk-1

    Calculate the perimeter. Please be accurate to within 0.01 units.


    Solution


  46. Question

    Consider the triangle with vertices at the following coordinates:

    plot of chunk unnamed-chunk-1

    Calculate the perimeter. Please be accurate to within 0.01 units.


    Solution


  47. Question

    Consider the triangle with vertices at the following coordinates:

    plot of chunk unnamed-chunk-1

    Calculate the perimeter. Please be accurate to within 0.01 units.


    Solution


  48. Question

    Consider the triangle with vertices at the following coordinates:

    plot of chunk unnamed-chunk-1

    Calculate the perimeter. Please be accurate to within 0.01 units.


    Solution


  49. Question

    Consider the triangle with vertices at the following coordinates:

    plot of chunk unnamed-chunk-1

    Calculate the perimeter. Please be accurate to within 0.01 units.


    Solution


  50. Question

    Consider the triangle with vertices at the following coordinates:

    plot of chunk unnamed-chunk-1

    Calculate the perimeter. Please be accurate to within 0.01 units.


    Solution


  51. Question

    An archery target is 200 millimeters wide. It is composed of concentric rings. The center ring is worth 10 points, the next ring is worth 9, and so on as shown in the diagram. Notice the radii of the rings are all multiples of 10 millimeters.

    By setting up a Cartesian coordinate system, with units of millimeters, and the origin at the bullseye, we can indicate any point on the target with a Cartesian-coordinate ordered pair.

    plot of chunk unnamed-chunk-1

    An archer shoots 36 arrows; the positions are indicated in the table below.

    x (mm) y (mm)
    -36 63
    -33 41
    65 18
    -5 33
    -20 -58
    -3 73
    -47 -17
    54 -21
    91 37
    -19 -9
    -46 10
    47 -21
    94 2
    95 2
    -16 -40
    -59 -36
    -22 -27
    -45 -10
    -22 4
    -44 -76
    -8 -20
    75 -29
    -86 50
    16 -42
    47 69
    53 -68
    39 -25
    -74 49
    -49 10
    -15 51
    29 9
    21 50
    -22 1
    -31 -62
    14 -17
    47 -30


    How many of these arrows landed in the ring worth 2 points?

    (Assume the arrows are infinitely skinny. None landed exactly on a boundary.)


    Solution


  52. Question

    An archery target is 200 millimeters wide. It is composed of concentric rings. The center ring is worth 10 points, the next ring is worth 9, and so on as shown in the diagram. Notice the radii of the rings are all multiples of 10 millimeters.

    By setting up a Cartesian coordinate system, with units of millimeters, and the origin at the bullseye, we can indicate any point on the target with a Cartesian-coordinate ordered pair.

    plot of chunk unnamed-chunk-1

    An archer shoots 36 arrows; the positions are indicated in the table below.

    x (mm) y (mm)
    79 21
    51 -41
    -45 21
    -47 18
    -9 -54
    -7 -49
    20 27
    48 -30
    -21 69
    38 60
    25 13
    92 -18
    -26 38
    -13 9
    8 38
    46 17
    -21 -39
    -33 4
    -21 17
    -28 23
    76 38
    4 -3
    -10 -9
    -33 42
    -21 29
    -3 -32
    -33 -27
    -34 -3
    21 30
    -41 -21
    -2 -53
    63 -11
    81 -14
    -35 27
    22 3
    -4 4


    How many of these arrows landed in the ring worth 2 points?

    (Assume the arrows are infinitely skinny. None landed exactly on a boundary.)


    Solution


  53. Question

    An archery target is 200 millimeters wide. It is composed of concentric rings. The center ring is worth 10 points, the next ring is worth 9, and so on as shown in the diagram. Notice the radii of the rings are all multiples of 10 millimeters.

    By setting up a Cartesian coordinate system, with units of millimeters, and the origin at the bullseye, we can indicate any point on the target with a Cartesian-coordinate ordered pair.

    plot of chunk unnamed-chunk-1

    An archer shoots 36 arrows; the positions are indicated in the table below.

    x (mm) y (mm)
    -9 21
    -43 -2
    26 30
    52 0
    23 15
    -29 -16
    -21 -29
    -32 12
    18 8
    3 -50
    29 62
    -52 -33
    -57 -16
    -34 70
    36 -24
    -25 -19
    -64 -51
    -29 18
    42 -60
    -28 -26
    -16 -8
    44 -24
    -39 8
    33 21
    -20 -34
    -8 -69
    5 3
    -15 -6
    2 -5
    -67 43
    -3 -23
    8 -9
    -6 23
    -48 44
    -50 11
    -22 31


    How many of these arrows landed in the ring worth 9 points?

    (Assume the arrows are infinitely skinny. None landed exactly on a boundary.)


    Solution


  54. Question

    An archery target is 200 millimeters wide. It is composed of concentric rings. The center ring is worth 10 points, the next ring is worth 9, and so on as shown in the diagram. Notice the radii of the rings are all multiples of 10 millimeters.

    By setting up a Cartesian coordinate system, with units of millimeters, and the origin at the bullseye, we can indicate any point on the target with a Cartesian-coordinate ordered pair.

    plot of chunk unnamed-chunk-1

    An archer shoots 36 arrows; the positions are indicated in the table below.

    x (mm) y (mm)
    21 -6
    -28 40
    -40 -55
    9 3
    -31 -7
    14 21
    -27 -14
    -3 52
    34 -47
    10 -32
    47 -4
    -54 -69
    -12 24
    18 63
    0 6
    -11 63
    12 53
    -15 57
    -47 -4
    5 -19
    62 -65
    -38 -12
    47 49
    -26 14
    -22 -97
    60 10
    14 -40
    18 -47
    9 -56
    -43 51
    -8 0
    20 -46
    -9 35
    -68 31
    38 -4
    20 7


    How many of these arrows landed in the ring worth 5 points?

    (Assume the arrows are infinitely skinny. None landed exactly on a boundary.)


    Solution


  55. Question

    An archery target is 200 millimeters wide. It is composed of concentric rings. The center ring is worth 10 points, the next ring is worth 9, and so on as shown in the diagram. Notice the radii of the rings are all multiples of 10 millimeters.

    By setting up a Cartesian coordinate system, with units of millimeters, and the origin at the bullseye, we can indicate any point on the target with a Cartesian-coordinate ordered pair.

    plot of chunk unnamed-chunk-1

    An archer shoots 36 arrows; the positions are indicated in the table below.

    x (mm) y (mm)
    1 40
    21 33
    -1 -74
    31 -14
    -27 -51
    18 76
    -57 -60
    32 9
    -29 -54
    8 14
    -70 54
    -35 -42
    20 -66
    1 -10
    11 -19
    -6 7
    32 -26
    17 -65
    5 -26
    32 40
    -33 -23
    58 39
    -37 -16
    -8 11
    -38 19
    79 11
    15 62
    10 31
    -49 50
    -11 -19
    17 -21
    -43 21
    -3 -4
    24 -42
    22 30
    -14 -23


    How many of these arrows landed in the ring worth 4 points?

    (Assume the arrows are infinitely skinny. None landed exactly on a boundary.)


    Solution


  56. Question

    An archery target is 200 millimeters wide. It is composed of concentric rings. The center ring is worth 10 points, the next ring is worth 9, and so on as shown in the diagram. Notice the radii of the rings are all multiples of 10 millimeters.

    By setting up a Cartesian coordinate system, with units of millimeters, and the origin at the bullseye, we can indicate any point on the target with a Cartesian-coordinate ordered pair.

    plot of chunk unnamed-chunk-1

    An archer shoots 36 arrows; the positions are indicated in the table below.

    x (mm) y (mm)
    35 69
    -12 51
    39 -22
    54 -6
    -55 21
    -85 23
    41 22
    -32 -55
    -22 -16
    18 17
    10 18
    11 12
    -23 48
    19 20
    -22 74
    -6 -24
    -61 -32
    -15 -25
    19 -17
    45 -38
    1 24
    7 18
    9 -32
    18 2
    -60 -56
    59 -18
    60 -1
    35 26
    9 -44
    69 11
    -27 -38
    -25 6
    -35 58
    10 -55
    22 54
    -25 -27


    How many of these arrows landed in the ring worth 8 points?

    (Assume the arrows are infinitely skinny. None landed exactly on a boundary.)


    Solution


  57. Question

    An archery target is 200 millimeters wide. It is composed of concentric rings. The center ring is worth 10 points, the next ring is worth 9, and so on as shown in the diagram. Notice the radii of the rings are all multiples of 10 millimeters.

    By setting up a Cartesian coordinate system, with units of millimeters, and the origin at the bullseye, we can indicate any point on the target with a Cartesian-coordinate ordered pair.

    plot of chunk unnamed-chunk-1

    An archer shoots 36 arrows; the positions are indicated in the table below.

    x (mm) y (mm)
    6 7
    -51 28
    80 -28
    -6 -54
    48 -7
    -18 41
    -43 -26
    -41 28
    -53 -54
    43 -18
    -33 -7
    3 13
    -27 -56
    19 -42
    1 -37
    -46 23
    -44 -3
    4 54
    7 -31
    17 -16
    -7 -11
    78 48
    -14 -33
    -7 22
    -41 -48
    49 -5
    37 17
    35 77
    33 13
    -7 -50
    -19 30
    36 42
    -30 -26
    3 -60
    -81 0
    18 -6


    How many of these arrows landed in the ring worth 4 points?

    (Assume the arrows are infinitely skinny. None landed exactly on a boundary.)


    Solution


  58. Question

    An archery target is 200 millimeters wide. It is composed of concentric rings. The center ring is worth 10 points, the next ring is worth 9, and so on as shown in the diagram. Notice the radii of the rings are all multiples of 10 millimeters.

    By setting up a Cartesian coordinate system, with units of millimeters, and the origin at the bullseye, we can indicate any point on the target with a Cartesian-coordinate ordered pair.

    plot of chunk unnamed-chunk-1

    An archer shoots 36 arrows; the positions are indicated in the table below.

    x (mm) y (mm)
    -17 7
    3 -34
    -19 -36
    -2 63
    47 22
    -62 -20
    53 10
    60 7
    27 -13
    -30 28
    29 11
    -46 -17
    7 21
    -10 -4
    -31 -48
    -1 -45
    30 30
    16 -66
    -30 31
    -14 11
    -6 -32
    -8 -19
    -10 -33
    -46 81
    -13 -41
    -8 3
    34 -11
    36 -32
    67 2
    9 -35
    -35 -4
    -55 1
    -18 17
    -32 -62
    -81 25
    -10 -14


    How many of these arrows landed in the ring worth 8 points?

    (Assume the arrows are infinitely skinny. None landed exactly on a boundary.)


    Solution


  59. Question

    An archery target is 200 millimeters wide. It is composed of concentric rings. The center ring is worth 10 points, the next ring is worth 9, and so on as shown in the diagram. Notice the radii of the rings are all multiples of 10 millimeters.

    By setting up a Cartesian coordinate system, with units of millimeters, and the origin at the bullseye, we can indicate any point on the target with a Cartesian-coordinate ordered pair.

    plot of chunk unnamed-chunk-1

    An archer shoots 36 arrows; the positions are indicated in the table below.

    x (mm) y (mm)
    -25 40
    -30 -35
    -46 -53
    18 5
    25 -1
    -11 34
    54 19
    -21 77
    -13 53
    -27 51
    -9 30
    23 -12
    52 -16
    -7 44
    -6 36
    39 13
    45 7
    -5 -2
    31 8
    47 -7
    13 -15
    28 13
    -7 55
    31 5
    15 46
    2 -14
    -11 34
    -37 35
    24 -7
    -33 28
    -79 -41
    40 17
    -37 -15
    -21 -21
    27 -48
    37 -46


    How many of these arrows landed in the ring worth 6 points?

    (Assume the arrows are infinitely skinny. None landed exactly on a boundary.)


    Solution


  60. Question

    An archery target is 200 millimeters wide. It is composed of concentric rings. The center ring is worth 10 points, the next ring is worth 9, and so on as shown in the diagram. Notice the radii of the rings are all multiples of 10 millimeters.

    By setting up a Cartesian coordinate system, with units of millimeters, and the origin at the bullseye, we can indicate any point on the target with a Cartesian-coordinate ordered pair.

    plot of chunk unnamed-chunk-1

    An archer shoots 36 arrows; the positions are indicated in the table below.

    x (mm) y (mm)
    -18 3
    62 3
    21 0
    52 -21
    10 4
    -29 61
    -1 -64
    5 57
    61 17
    24 3
    17 -6
    -34 15
    39 1
    9 -30
    -21 34
    12 20
    35 8
    -2 38
    25 -7
    10 5
    -36 -49
    -9 -6
    26 -9
    10 -27
    24 -43
    36 -60
    -50 -35
    5 -13
    -21 14
    18 -31
    81 -45
    -9 -62
    36 -6
    1 -19
    -17 22
    -1 -32


    How many of these arrows landed in the ring worth 7 points?

    (Assume the arrows are infinitely skinny. None landed exactly on a boundary.)


    Solution


  61. Question

    A right rectangular prism is 17 inches wide, 11 inches deep, and 20 inches tall.

    What is the distance between opposite corners?

    plot of chunk unnamed-chunk-1

    Please be accurate within \(\pm\) 0.01 of the exact answer.


    Solution


  62. Question

    A right rectangular prism is 18 inches wide, 13 inches deep, and 8 inches tall.

    What is the distance between opposite corners?

    plot of chunk unnamed-chunk-1

    Please be accurate within \(\pm\) 0.01 of the exact answer.


    Solution


  63. Question

    A right rectangular prism is 18 inches wide, 6 inches deep, and 10 inches tall.

    What is the distance between opposite corners?

    plot of chunk unnamed-chunk-1

    Please be accurate within \(\pm\) 0.01 of the exact answer.


    Solution


  64. Question

    A right rectangular prism is 17 inches wide, 19 inches deep, and 15 inches tall.

    What is the distance between opposite corners?

    plot of chunk unnamed-chunk-1

    Please be accurate within \(\pm\) 0.01 of the exact answer.


    Solution


  65. Question

    A right rectangular prism is 5 inches wide, 11 inches deep, and 9 inches tall.

    What is the distance between opposite corners?

    plot of chunk unnamed-chunk-1

    Please be accurate within \(\pm\) 0.01 of the exact answer.


    Solution


  66. Question

    A right rectangular prism is 17 inches wide, 9 inches deep, and 13 inches tall.

    What is the distance between opposite corners?

    plot of chunk unnamed-chunk-1

    Please be accurate within \(\pm\) 0.01 of the exact answer.


    Solution


  67. Question

    A right rectangular prism is 15 inches wide, 14 inches deep, and 18 inches tall.

    What is the distance between opposite corners?

    plot of chunk unnamed-chunk-1

    Please be accurate within \(\pm\) 0.01 of the exact answer.


    Solution


  68. Question

    A right rectangular prism is 20 inches wide, 9 inches deep, and 13 inches tall.

    What is the distance between opposite corners?

    plot of chunk unnamed-chunk-1

    Please be accurate within \(\pm\) 0.01 of the exact answer.


    Solution


  69. Question

    A right rectangular prism is 12 inches wide, 19 inches deep, and 16 inches tall.

    What is the distance between opposite corners?

    plot of chunk unnamed-chunk-1

    Please be accurate within \(\pm\) 0.01 of the exact answer.


    Solution


  70. Question

    A right rectangular prism is 8 inches wide, 18 inches deep, and 14 inches tall.

    What is the distance between opposite corners?

    plot of chunk unnamed-chunk-1

    Please be accurate within \(\pm\) 0.01 of the exact answer.


    Solution


  71. Question

    When plotting all \(x\)-\(y\) pairs that satisfy the given equation (make the equation true), the result is a circle.

    \[x^2+6x+y^2-8y~=~-21\]

    The standard form of an equation of a circle shows the center \((h,k)\) and radius \(r\) as parameters.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    In order to convert the given circle into standard form, you should complete the square (twice, once for \(x\)-containing terms and once for \(y\)-containing terms). After you convert the equation to standard form, indicate the values of the parameters.



    Solution


  72. Question

    When plotting all \(x\)-\(y\) pairs that satisfy the given equation (make the equation true), the result is a circle.

    \[x^2-4x+y^2+12y~=~-31\]

    The standard form of an equation of a circle shows the center \((h,k)\) and radius \(r\) as parameters.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    In order to convert the given circle into standard form, you should complete the square (twice, once for \(x\)-containing terms and once for \(y\)-containing terms). After you convert the equation to standard form, indicate the values of the parameters.



    Solution


  73. Question

    When plotting all \(x\)-\(y\) pairs that satisfy the given equation (make the equation true), the result is a circle.

    \[x^2-18x+y^2-12y~=~-113\]

    The standard form of an equation of a circle shows the center \((h,k)\) and radius \(r\) as parameters.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    In order to convert the given circle into standard form, you should complete the square (twice, once for \(x\)-containing terms and once for \(y\)-containing terms). After you convert the equation to standard form, indicate the values of the parameters.



    Solution


  74. Question

    When plotting all \(x\)-\(y\) pairs that satisfy the given equation (make the equation true), the result is a circle.

    \[x^2+4x+y^2-10y~=~52\]

    The standard form of an equation of a circle shows the center \((h,k)\) and radius \(r\) as parameters.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    In order to convert the given circle into standard form, you should complete the square (twice, once for \(x\)-containing terms and once for \(y\)-containing terms). After you convert the equation to standard form, indicate the values of the parameters.



    Solution


  75. Question

    When plotting all \(x\)-\(y\) pairs that satisfy the given equation (make the equation true), the result is a circle.

    \[x^2-8x+y^2-10y~=~-32\]

    The standard form of an equation of a circle shows the center \((h,k)\) and radius \(r\) as parameters.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    In order to convert the given circle into standard form, you should complete the square (twice, once for \(x\)-containing terms and once for \(y\)-containing terms). After you convert the equation to standard form, indicate the values of the parameters.



    Solution


  76. Question

    When plotting all \(x\)-\(y\) pairs that satisfy the given equation (make the equation true), the result is a circle.

    \[x^2+18x+y^2+10y~=~-97\]

    The standard form of an equation of a circle shows the center \((h,k)\) and radius \(r\) as parameters.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    In order to convert the given circle into standard form, you should complete the square (twice, once for \(x\)-containing terms and once for \(y\)-containing terms). After you convert the equation to standard form, indicate the values of the parameters.



    Solution


  77. Question

    When plotting all \(x\)-\(y\) pairs that satisfy the given equation (make the equation true), the result is a circle.

    \[x^2-10x+y^2+12y~=~-45\]

    The standard form of an equation of a circle shows the center \((h,k)\) and radius \(r\) as parameters.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    In order to convert the given circle into standard form, you should complete the square (twice, once for \(x\)-containing terms and once for \(y\)-containing terms). After you convert the equation to standard form, indicate the values of the parameters.



    Solution


  78. Question

    When plotting all \(x\)-\(y\) pairs that satisfy the given equation (make the equation true), the result is a circle.

    \[x^2+8x+y^2+14y~=~16\]

    The standard form of an equation of a circle shows the center \((h,k)\) and radius \(r\) as parameters.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    In order to convert the given circle into standard form, you should complete the square (twice, once for \(x\)-containing terms and once for \(y\)-containing terms). After you convert the equation to standard form, indicate the values of the parameters.



    Solution


  79. Question

    When plotting all \(x\)-\(y\) pairs that satisfy the given equation (make the equation true), the result is a circle.

    \[x^2-16x+y^2-10y~=~-40\]

    The standard form of an equation of a circle shows the center \((h,k)\) and radius \(r\) as parameters.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    In order to convert the given circle into standard form, you should complete the square (twice, once for \(x\)-containing terms and once for \(y\)-containing terms). After you convert the equation to standard form, indicate the values of the parameters.



    Solution


  80. Question

    When plotting all \(x\)-\(y\) pairs that satisfy the given equation (make the equation true), the result is a circle.

    \[x^2-4x+y^2+18y~=~-76\]

    The standard form of an equation of a circle shows the center \((h,k)\) and radius \(r\) as parameters.

    \[(x-h)^2+(y-k)^2~=~r^2\]

    In order to convert the given circle into standard form, you should complete the square (twice, once for \(x\)-containing terms and once for \(y\)-containing terms). After you convert the equation to standard form, indicate the values of the parameters.



    Solution


  81. Question

    Consider the two points:

    A third collinear point, \(C\), is 40% of the way from point \(A\) to point \(B\), as shown below. .

    plot of chunk unnamed-chunk-1

    Find the coordinates of point \(C\):

    (,)



    Solution


  82. Question

    Consider the two points:

    A third collinear point, \(C\), is 60% of the way from point \(A\) to point \(B\), as shown below. .

    plot of chunk unnamed-chunk-1

    Find the coordinates of point \(C\):

    (,)



    Solution


  83. Question

    Consider the two points:

    A third collinear point, \(C\), is 20% of the way from point \(A\) to point \(B\), as shown below. .

    plot of chunk unnamed-chunk-1

    Find the coordinates of point \(C\):

    (,)



    Solution


  84. Question

    Consider the two points:

    A third collinear point, \(C\), is 60% of the way from point \(A\) to point \(B\), as shown below. .

    plot of chunk unnamed-chunk-1

    Find the coordinates of point \(C\):

    (,)



    Solution


  85. Question

    Consider the two points:

    A third collinear point, \(C\), is 40% of the way from point \(A\) to point \(B\), as shown below. .

    plot of chunk unnamed-chunk-1

    Find the coordinates of point \(C\):

    (,)



    Solution


  86. Question

    Consider the two points:

    A third collinear point, \(C\), is 80% of the way from point \(A\) to point \(B\), as shown below. .

    plot of chunk unnamed-chunk-1

    Find the coordinates of point \(C\):

    (,)



    Solution


  87. Question

    Consider the two points:

    A third collinear point, \(C\), is 20% of the way from point \(A\) to point \(B\), as shown below. .

    plot of chunk unnamed-chunk-1

    Find the coordinates of point \(C\):

    (,)



    Solution


  88. Question

    Consider the two points:

    A third collinear point, \(C\), is 40% of the way from point \(A\) to point \(B\), as shown below. .

    plot of chunk unnamed-chunk-1

    Find the coordinates of point \(C\):

    (,)



    Solution


  89. Question

    Consider the two points:

    A third collinear point, \(C\), is 80% of the way from point \(A\) to point \(B\), as shown below. .

    plot of chunk unnamed-chunk-1

    Find the coordinates of point \(C\):

    (,)



    Solution


  90. Question

    Consider the two points:

    A third collinear point, \(C\), is 40% of the way from point \(A\) to point \(B\), as shown below. .

    plot of chunk unnamed-chunk-1

    Find the coordinates of point \(C\):

    (,)



    Solution